An Isaac Newton Institute Workshop

The Theory of Highly Oscillatory Problems

Conservation of energy and actions in numerical discretizations of nonlinear wave equations

Abstract

For numerical discretizations of nonlinearly perturbed
wave equations the long-time near-conservation of
energy, momentum, and harmonic actions is studied.
The proofs are based on the technique of
modulated Fourier expansions in time.
Rigorous statements on the
long-time conservation properties are shown
under suitable numerical non-resonance conditions and
under a CFL condition. The time step need not
be small compared to the inverse of the largest
frequency in the space-discretized system.